# Research on Hydraulic Properties and Energy Dissipation Mechanism of the Novel Water-Retaining Labyrinth Channel Emitters

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Structure Design and Physical Model

#### 2.2. Mathematical Model of the CWRLC Emitter

#### 2.3. Meshing and Simulation Parameters Setting

#### 2.4. Experimental Test

## 3. Results

#### 3.1. Influence of Hydraulic Performance

_{r}

_{= 0.90 mm}increased from 2.654 L/h to 3.850 L/h and the increment of 1.196 L/h with a growth rate of 45.08%; whereas, when the inlet pressure increased from 180 KPa to 200 KPa, the average outlet flow rate of CWRLC

_{r}

_{= 0.90 mm}increased from 8.586 L/h to 9.082 L/h and only the increment of 0.496 L/h with a growth rate of 5.78%,the reason that the viscous resistance and impact force of water along the CWRLC emitter wall increased with the rise of the working pressure and the flow velocity, resulting in a large loss of flow energy and decrease in growth rate. For the same inlet pressure, the average outlet flow rate of the CWRLC emitter decreased with the increase in the parameters r. For each 0.05-mm increase in the parameters r, the average outlet flow rate decreased by about 0.35 L/h. This caused the flow in the cross-sectional area to be reduced with the increase in the parameters r, leading to a decrease in the average outlet flow rate.

^{2}) of CWRLC

_{r}

_{= 0.90 mm}, CWRLC

_{r}

_{= 0.95 mm}, CWRLC

_{r}

_{= 1.00 mm}, CWRLC

_{r}

_{= 1.05 mm}, CWRLC

_{r}

_{= 1.10 mm}, and CWRLC

_{r}

_{= 1.15 mm}were 0.99999, 0.99999, 0.99999, 0.99998, 0.99992, and 0.99982, respectively, which all reached a significant level (R

^{2}> 0.8). The flow index x of the CWRLC emitter increased with the rise of the parameters r, demonstrating that the average outlet flow rate became more sensitive to the change of the working pressure. When r = 0.90 mm, the flow index of the CWRLC emitter was 0.5334; when r = 1.15 mm, the flow index of the CWRLC emitter was 0.5719. The reason that the boundary wall constraint on the water flow decreased with the rise of the parameters r, leading to an increase in sensitivity of the average outlet flow rate to the working pressure. Therefore, it is necessary to further analyze the internal flow field in the flow channel.

#### 3.2. Analysis of Flow Channel Internal Flow Characteristics

_{A}or C

_{B}) and low-speed vortex area (D

_{A}or D

_{B}). The flow velocity in area C

_{A}was obviously higher than that in area C

_{B}. The maximum flow velocities of CWRLC

_{r}

_{= 0.90 mm}, CWRLC

_{r}

_{= 0.95 mm}, CWRLC

_{r}

_{= 1.00 mm}, CWRLC

_{r}

_{= 1.05 mm}, CWRLC

_{r}

_{= 1.10 mm}, and CWRLC

_{r}

_{= 1.15 mm}were 4.47 m/s, 4.32 m/s, 4.14 m/s, 4.02 m/s, 3.67 m/s, and 3.22 m/s, respectively. The maximum flow velocity decreased with the increase in the parameters r.

_{A}or D

_{B}) also decreased with the rise of the parameters r from the velocity vector distribution. The water flow in this area formed a large vortex and eddy between the boundary wall of the flow channel and mainstream area. The energy of the water flow in the flow channel was fully expended by the vortex flow. The proportion of the vortex area (D

_{A}or D

_{B}) determined the constraint ability of the boundary wall to the water flow. The larger the proportion of the vortex area (D

_{A}or D

_{B}), the greater the constraint ability of the boundary wall to the water flow. Obviously, the proportion of the vortex area (D

_{A}or D

_{B}) of CWRLC

_{r}

_{=0.90 mm}in the flow channel was largest, and the CWRLC

_{r}

_{= 1.15 mm}was the smallest.

_{A}, C

_{A}, D

_{A}, C

_{A}, C

_{B}, D

_{B}, C

_{B}, and D

_{B}areas successively. We defined the crests as C

_{A1}, C

_{AB}, and C

_{B1}, respectively. The troughs were defined as D

_{A1}, D

_{A2}, D

_{B1}, and D

_{B2}, respectively. In the CWRLC

_{r}

_{= 0.90 mm}internal flow field, the speed of C

_{A1}(2.76 m/s) was greater than that of C

_{AB}(2.25 m/s) due to the sufficient generation of low-speed vortex areas. However, the velocity of C

_{A1}(2.12 m/s) was less than that of C

_{AB}(2.65 m/s) in the CWRLC

_{r}

_{= 1.15 mm}internal flow field. This means that the flow channel of CWRLC

_{r}

_{=0.90 mm}consumed more water flow energy than CWRLC

_{r}

_{= 1.15 mm}. It was also sufficient to indicate that the proportion of the low-speed vortex areas played a critical role in the energy consumption capacity of the flow channel. The larger the proportion of low-speed vortex areas, the more obvious the energy dissipation. This was a fundamental reason why the flow index increased with the rise of the parameters r. Therefore, the increase in the proportion of the low-speed vortex area (D) could reduce the flow index, thereby improving the hydraulic performance and energy dissipation of the drip irrigation emitter.

#### 3.3. Structure Optimization of the Flow Channel

_{r}

_{= 0.90 mm}flow channel structure.

^{2}) were 0.9999, 0.9999, 0.9999, and 0.9994, respectively. The flow indexes of the four emitters were 0.5334, 0.5041, 0.4796, and 0.4917, respectively. Among them, the SWRLC emitter had the lowest flow pattern index. The values of the flow index of the QWRLC and SWRLC emitters were decreased by 5.49% and 10.09%, respectively, compared with that of the CWRLC emitter by analyzing the internal flow field and optimizing the structure. In particular, the value of the flow index of the improved emitter SWRLC was 2.46% lower than that of the widely used emitter, TLC. Therefore, the novel SWRLC emitter had a better hydraulic performance and irrigation uniformity.

#### 3.4. Experimental Verification of Hydraulic Performance for Drip Emitters

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**The mid-depth cross sectional velocity vector distributions of the fourth flow channel unit for six flow channels under 100 KPa.

**Figure 7.**The velocity line diagram of the center line of the mid-depth cross-section for six flow channels.

**Figure 9.**Simulation results of the velocity vector distributions in two improved flow channel structures under 100 KPa.

**Figure 10.**Schematic diagram and velocity vector distribution of the flow channel structures under 100 KPa.

Trapezoid Baseline Length s (mm) | Trapezoid Height h (mm) | Radius of Circular Water-Retaining r (mm) | Angle between Hypotenuses of Adjacent Trapezoids $\mathit{\theta}$ (°) | Channel Depth d (mm) | The Number of Channel Units n |
---|---|---|---|---|---|

2.50 | 0.80 | 0.90; 0.95; 1.00 1.05; 1.10; 1.15 | 54 | 1.50 | 15 |

r (mm) | Flow Rate (L/h) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

20 KPa | 40 KPa | 60 KPa | 80 KPa | 100 KPa | 120 KPa | 140 KPa | 160 KPa | 180 KPa | 200 KPa | |

0.90 | 2.654 | 3.850 | 4.781 | 5.573 | 6.277 | 6.917 | 7.509 | 8.063 | 8.586 | 9.082 |

0.95 | 2.335 | 3.393 | 4.216 | 4.915 | 5.536 | 6.101 | 6.623 | 7.113 | 7.575 | 8.014 |

1.00 | 2.006 | 2.925 | 3.638 | 4.244 | 4.782 | 5.270 | 5.722 | 6.144 | 6.542 | 6.921 |

1.05 | 1.670 | 2.451 | 3.056 | 3.570 | 4.026 | 4.440 | 4.821 | 5.178 | 5.515 | 5.834 |

1.10 | 1.319 | 1.962 | 2.461 | 2.885 | 3.260 | 3.600 | 3.914 | 4.208 | 4.484 | 4.746 |

1.15 | 0.946 | 1.440 | 1.828 | 2.158 | 2.451 | 2.718 | 2.963 | 3.193 | 3.409 | 3.614 |

Emitters | Flow Rate (L/h) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

20 KPa | 40 KPa | 60 KPa | 80 KPa | 100 KPa | 120 KPa | 140 KPa | 160 KPa | 180 KPa | 200 KPa | |

CWRLC | 2.588 | 3.716 | 4.721 | 5.491 | 6.237 | 6.922 | 7.571 | 8.180 | 8.706 | 9.207 |

QWRLC | 3.150 | 4.428 | 5.467 | 6.245 | 7.037 | 7.688 | 8.328 | 8.906 | 9.463 | 9.950 |

SWRLC | 3.449 | 4.641 | 5.651 | 6.483 | 7.237 | 7.880 | 8.499 | 9.106 | 9.626 | 10.09 |

TLC | 2.054 | 2.826 | 3.498 | 3.992 | 4.443 | 4.860 | 5.255 | 5.615 | 5.942 | 6.230 |

**Table 4.**Statistical analysis of the differences of the emitter flow rate using Tukey’s method at 200 KPa.

Emitters (I) | Emitters (J) | Means (I) | Means (J) | Differences (I-J) | p-Value |
---|---|---|---|---|---|

CWRLC | QWRLC | 9.207 | 9.950 | −0.742 | 0.001 |

CWRLC | SWRLC | 9.207 | 10.09 | −0.882 | 0.001 |

CWRLC | TLC | 9.207 | 6.230 | 2.978 | 0.001 |

QWRLC | SWRLC | 9.950 | 10.09 | −0.140 | 0.058 |

QWRLC | TLC | 9.950 | 6.230 | 3.720 | 0.001 |

SWRLC | TLC | 10.09 | 6.23 | 3.860 | 0.001 |

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**MDPI and ACS Style**

Li, Y.; Feng, X.; Liu, Y.; Han, X.; Liu, H.; Sun, Y.; Li, H.; Xie, Y.
Research on Hydraulic Properties and Energy Dissipation Mechanism of the Novel Water-Retaining Labyrinth Channel Emitters. *Agronomy* **2022**, *12*, 1708.
https://doi.org/10.3390/agronomy12071708

**AMA Style**

Li Y, Feng X, Liu Y, Han X, Liu H, Sun Y, Li H, Xie Y.
Research on Hydraulic Properties and Energy Dissipation Mechanism of the Novel Water-Retaining Labyrinth Channel Emitters. *Agronomy*. 2022; 12(7):1708.
https://doi.org/10.3390/agronomy12071708

**Chicago/Turabian Style**

Li, Yanfei, Xianying Feng, Yandong Liu, Xingchang Han, Haiyang Liu, Yitian Sun, Hui Li, and Yining Xie.
2022. "Research on Hydraulic Properties and Energy Dissipation Mechanism of the Novel Water-Retaining Labyrinth Channel Emitters" *Agronomy* 12, no. 7: 1708.
https://doi.org/10.3390/agronomy12071708